When the brakes are applied on a vehicle traveling at a given velocity, braking torques are generated at each of the braked wheels. The braking torque causes a retarding or braking force to be generated at the interface between the tire and the surface. The braking forces generated at the wheels then cause a decrease in the vehicle velocity.
Ideally, the braking forces at the wheels increase proportionately as the driver increases the force on the brake pedal. Unfortunately, this is not always the case in braking procedures. As the braking torque and hence the braking force at the wheel is increased, the rotational speed of the braked wheels becomes less than the speed of the vehicle. When the rotational speed of a wheel is less than the vehicle speed, "slippage" is said to occur between the tire and the surface. With further increase in brake pressure, the slippage between the tire and the surface increases until lock-up and skidding of the wheel occurs. In most cases, lock-up causes a reduction in braking force and an increase in stopping distance. Lock-up also causes a degradation in directional control due to a reduction in the lateral forces at the wheels.
Both of these problems associated with lock-up were addressed with the advent of anti-lock brake systems (ABS). A basic anti-lock brake system monitors the velocity at the each of the wheels, decides whether the wheel is excessively slipping based on these velocity measurements, and modulates the braking pressure accordingly to avoid lock-up. The ABS aids in retaining vehicle stability and steerability while providing shorter stopping distances.
One method by which a state of excessive slippage is identified in the ABS is comparing the velocity of each wheel to a reference speed. The reference speed is an estimate of the true vehicle speed based on current and previous values of the individual wheel velocities. If the velocity of a wheel is significantly less than the reference speed, then the wheel is deemed by the ABS to be excessively slipping. The ABS then reduces the pressure actuating the brake in order to reduce brake torque. The reduction of brake torque allows the friction force at the surface to accelerate the wheel, thereby causing a reduction of the slip in the wheel.
After a period of constant braking pressure following the pressure reduction, the pressure actuating the brake is increased until excessive wheel slip occurs again. The cycle of decreasing the brake pressure, maintaining constant brake pressure, and then increasing brake pressure is repeated until the anti-lock event ends. The parameters which define the specifics of this cycle depend on both the vehicle and the surface conditions.
For the present invention, the braking of a vehicle on a surface with varying coefficient of friction is considered. The coefficient of friction, mu, of a surface is defined as the ratio of the braking force generated at the interface between the tire and the surface, to the normal force between the tire and the surface.
Three classes of surfaces can be defined qualitatively in terms of mu: high-mu, low-mu, and split-mu. A high-mu surface is one which produces relatively good braking ability. Dry asphalt is an example of a high-mu surface. A low-mu surface is characterized by its resulting in poor braking ability. An example of a low-mu surface is a road covered with snow or ice. A split-mu surface is encountered when a vehicle has some of its tires on a low-mu surface and the other tires on a high-mu surface. An example of a split-mu surface is a road with snow or ice on one side of the vehicle and dry asphalt on the other side of the vehicle.
An example of braking on a low-mu to split-mu transition can be envisaged based on the previous examples. Consider a vehicle braking on a snow-covered surface. Suppose that during the braking procedure, the left tires become exposed to a cleared section of the road (e.g., asphalt) while the right tires are still exposed to snow. In this situation, the vehicle would be pulled to the high-mu side (here, the left side) of the road because of the increased braking force on the newly high-mu wheel. The driver would then have to provide corrective steering measures to maintain the intended direction of the vehicle.
The need exists within an anti-lock brake system for reducing the pull to the newly high-mu side of a vehicle braking on a low-mu to split-mu transition.